The blasts come in the wake of a series of high-intensity attacks since the arrival of top US official Paul Wolfowitz to Iraq.
The dead included four Iraqi policemen while the injured included 10 US soldiers and seven Iraqi police personnel, according to medical sources, police and the US military.
US soldiers killed
Earlier on Sunday night, a roadside bomb and a mortar attack killed three US soldiers.
The roadside bomb killed two US soldiers who were on night patrol in the Iraqi capital, a US military spokesman said on Monday.
Another US soldier was killed on the western outskirts of Baghdad by a mortar attack about half an hour later. Two other soldiers were injured in the attack at around 10 pm on Sunday.
On Monday morning, there were five explosions which targeted four police stations and the offices of the International Committee of the Red Cross (ICRC), said US Brigadier General Mark Hertling.
The impact of the explosions was maximum as it happened during the rush hour.
The blast near the ICRC building killed 12 people and wounded at least 15, an ICRC official said. One witness said the bomb appeared to have been packed into an ambulance.
In the rubble
In the northeast of the Iraqi capital, a US military policeman said seven people had been killed in a blast near a police station.
Journalists at the scene of the explosion saw four people carried out of the rubble, but it was not clear if any of them were alive.
The car bomb exploded killing several officers outside a police station in Baghdad's Karkh neighbourhood, a policeman said.
A white car drew up at the al-Elam police station and exploded at 8:30 am (0530 GMT), policeman Abd al-Zahar Salim said.
Chaos reigned as the blasts
struck the heart of Baghdad
"We found many pieces of my colleagues on the ground," he said, as flesh was still scattered over the asphalt where 16 burnt-out vehicles smouldered and ambulances sped to the station.
The car crashed into the station's parking lot and burst into flames, as 40 policemen gathered to start work.
Two American military vehicles were in the lot and two US soldiers were also there, he said.
A US military policeman said eight people were killed. "There are eight dead, several walking wounded," Sergeant Mike Toole said.
Reuters photographer Akram Salih said he had counted 12 bodies at a central Baghdad hospital, where officials said one belonged to a foreigner whose nationality was unclear.
Witnesses said the first blast went off at about 8.30 am (0530 GMT), when a car drove towards the ICRC building.
"I was standing at the gate when a car came driving very fast and smashed against the wall and exploded," said an ICRC guard who gave his name as Sabah.
"I saw an ambulance car coming very fast towards the barrier and it exploded," another guard said.
ICRC official Pascal Jansen told reporters 10 people had been killed. "The death toll is 10 - two Iraqi guards working for the Red Cross and eight casual labourers going past in a lorry."
He said 15 Iraqi staff of the ICRC had been wounded, while international staff had only superficial injuries.
Another Reuters photographer said he saw at least three bodies lying among debris near the ICRC explosion.
"The force of the blast was so huge their clothes were blown right off," the photographer Chris Helgren said.
An Iraqi woman said two of her children had been wounded in the same explosion. "We were sleeping and the house came down on our heads," Muntaha Khalil said.
Witnesses to another blast said they had seen a vehicle heading towards a police station in the Baya district in southwest Baghdad.
The blasts were an unforgettable
start to the month of Ramadan
"It was a Landcruiser car that was speeding towards the police station. The (guards) fired on it four times. It turned right and blew up," local resident Muhammad Ali said.
Three wrecked cars were outside the building, one of them completely destroyed. A car engine lay smoking nearby.
The explosions plunged the city into chaos on the first day of the holy Muslim fasting month of Ramadan, as ambulance sirens wailed and black smoke billowed into the air.
A US military spokesman confirmed there had been a series of blasts, but had no details.
The blasts occurred a day after several rockets smashed into al-Rashid hotel, inside a heavily fortified compound which also houses the headquarters of the United States-led occupation administration.
"I saw an ambulance car coming very fast towards the barrier and it exploded"
Visiting US Deputy Defence Secretary Paul Wolfowitz was at the hotel during the attack and narrowly escaped.
But a US colonel was killed and 17 people wounded in the attack on the heart of American power in Iraq.
Two explosions followed the attack later on Sunday. No casualties were reported from these blasts.
Previous attacks on the UN headquarters and the Turkish and Jordanian embassies have underlined the increasing resistance US-led forces are facing in Iraq.
Sunday night’s death of the US soldier brings to 112 the number of occupation troops killed in Iraq since US President George Bush declared combat operations over on 1 May.